A substance $A_x{B}_y$ crystallizes in a face centered cubic lattice in which atoms A occupy each corner of the cube and atoms B occupy the centers of each face of the cube. Identify the correct composition of the substance $A_x{B}_y$.

${\mathrm{A}}_{\mathrm{x}}{\mathrm{B}}_{\mathrm{y}}$ forms a face-centered cubic ($\mathrm{FCC}$) lattice as it crystallizes.

Each corner of the cube is occupied by an atom. The result is that A has $8\times \frac{1}{8}=1$atoms.

Each face of the cube has a central cluster of B atoms. The total number of atoms in B is therefore $6\times \frac{1}{2}=3$.

Consequently, the equation becomes ${\mathrm{AB}}_3$